It is human nature to prefer immediate gratification. We dislike postponing consumption. If we are requested to delay our satisfaction, we demand a reward. This reward often takes the form of increased consumption at the later time. This same idea applies to money. Money, it has been observed, is only as good as what you can use it for. Whether dollars, rubles, or drachmas, money is a measure of the ability to consume. If we lend money we give up the possible immediate consumption it represents, and we expect a reward in the form of a greater return than the amount originally lent. In the case of money, the reward, or difference between what was lent and what is returned, is referred to as interest. Alternately, interest may be considered as rent.

A similar argument for interest is that the money could have been used to purchase assets. Those assets could then be rented to other parties (or used directly to produce a return). Interest, then, is compensation for rent or return foregone. More directly, interest is the cost of "renting" the money itself.

For reasons of comparability, interest is normally specified as a
percentage rate of increase, rather than as an absolute amount. The
"interest rate" is the percentage increase:

The interest rate is also sometimes described in terms of "basis points," with one basis point being one hundredth of 1 percent. The difference between the interest rate of 10.25 percent and the interest rate of 10.00 percent is 25 basis points.

The specification of the interest rate is not complete unless the period over which the increase occurs is specified. Although interest rates are stated in terms of an annual rate, interest may be computed and become due more often than annually. The period over which interest is calculated is called the compounding period. The standard period for compounding is one year, but other intervals such as quarterly, daily, or even continuous compounding are not unusual.

Where the compounding period is shorter than one year, the per period rate
must be converted to an annual rate. The simplest method of annualizing is
called "simple interest" or annual percentage rate (APR),
which is computed by simply multiplying the per period rate by the number
of periods in a year. The "yield" or interest rate on
**
bonds,
**
for instance, is normally computed on a semiannual basis and then
converted to an annual rate by multiplying by two. Although this rate is
incorrect when the compounding period is less than one year, it has become
convention, a holdover from days of hand calculation. The realized or
"effective" annual interest rate will be higher than the
stated annual rate due to the interest on interest effect. For example,
suppose that $100 is borrowed at 10 percent compounded semiannually. At
the end of six months, $50 is paid. The reduces the amount in the hands of
the borrower over the next six months to $95.00. The borrower thus pays
$10.00 annual interest to borrow an average of $97.50—an actual
rate of about 10.25 percent. Alternately, if $100.00 is invested for one
year at 6 percent compounded annually, the lender will receive $106.00 at
the end of the year, a return of 6 percent to the lender. The same $100.00
invested at 6 percent compounded semiannually would lead to interest
payments of $3.00 at six months and at one year. The $3.00 payment
received at six months would be added to the principal amount and
reinvested at 6 percent, however, so that the interest payment over the
second six months would be $3.30. Under semiannual compounding, the
investor's account at the end of the year would have the original
investment of $100.00, the six-month interest payment of $3.00, and the
one-year interest payment of $3.30—a total of $106.30. This would
be an actual or realized rate of return of 6.3 percent. The extra $0.30 is
interest on the interest. The effect of interest on interest and
compounding more often than once a period is not large for any one period,
but over long periods the realized amount can be significantly different.
If the above $100.00 had been invested at 6 percent for 20 years at simple
interest—i.e., with no compounding, ignoring reinvestment of
interest payments—the final amount would be the original $100.00,
plus 20 years' interest payments amounting to $120.00, a total of
$220.00. If the interest payments are reinvested at 6 percent compounded
annually, the final amount would be $320.71, with interest on interest
amounting to $100.71. The same $100 invested for 20 years at 6 percent
compounded semiannually would increase to $326.20. The $5.49 increase over
the amount earned under annual compounding would arise from interest on
interest.

The interest rate computation that includes the compounding effect is
called the annual percentage yield (APY), and is considered a superior
measure of annualized interest rates. The APY is computed by compounding
or multiplying the per period rates over the year to arrive at the
effective annual rate:

Another misleading form of interest computation is "discounted in advance." In this form, the interest is deducted from the principal, and the borrower receives the net amount. This form can severely understate the interest rate. In our example, a one-year borrower would receive $9.00, or $10.00 principal less $1.00 interest for one year, and would owe $10.00 at the end of the year, effectively paying the interest at the time of borrowing. This is equivalent to paying $1.00 to borrow $9.00, a compound annual rate of 11.11 percent.

LEVELS

The level of interest rates is set by supply and demand—i.e., when
the amount of money supplied is equal to the amount that other economic
units wish to borrow. The interesting question, however, is what factors
influence supply and demand. Since interest is in the nature of a reward
for postponing consumption, a higher interest rate can be expected to
result in a greater supply of funds. Under different conditions, however,
a given interest rate may result in a differing supply. Attitudes toward
consumption are important, as shown by the differences between savings
rates in different countries. Uncertainty about the economy may prompt
more saving, as shown by the different attitudes of the "depression
generation" and their children. Demand, on the other hand, depends
on the investments available, and will be downward sweeping since more
investments are profitable at lower interest rates. In periods of high
growth or technological advancement, there will be more acceptable
investment and greater demand. Future economic growth is affected by the
rate of increase of population, the
**
workforce,
**
and the educational and skill level. Economic conditions and production
possibilities set the general level of demand for funds.

The economic and other variables set the interest rate as a rate of
increase in ability to consume. This rate of increase in ability to
consume is called the "real" rate of interest. The
"nominal" or dollar rate of interest measures the increase
in dollars. Money is a measure of ability to consume, but the yardstick
itself changes over time due to
**
inflation.
**
Inflation is a decrease in the purchasing power, or amount of consumption
that can be acquired per monetary unit. Since it is the real rate of
interest that controls the supply and demand of funds, the nominal
interest rate
must include a premium that compensates for any expected loss of
purchasing power. The stated or nominal interest rate is then expressed as
the real rate of interest plus an inflation premium:

where
*
R
_{
N
}
*
= the nominal rate of interest,

I = the expected rate of inflation.

For small rates of inflation the inflation rate itself is a good approximation of the premium required, and the last term is often ignored. For higher rates of inflation the last term becomes significant, and should be included. The higher level of interest rates in the early 1980s is partially due to the effects of actual or feared inflation.

Interest rates are also affected by and are an instrument of government
policy. The
**
Federal Reserve
**
manages the amount of money in circulation, and affects the interest
rates. Too rapid growth of the amount of money will have an immediate
effect of decreasing interest rates, since supply is increased. Over the
longer run, however, too rapid growth in the amount of money may result in
inflation. Interest rates, reacting to the expectation of inflation, will
increase. Too low a rate of growth in the amount of money, on the other
hand, will result in a reduction of supply and higher interest rates. This
in turn may hamper economic growth. If the economy stagnates, the eventual
result may well be decreased interest rates.

Over time the Federal Reserve has placed varied emphasis on two policy
targets. The first is the growth of the amount of money, while the second
is interest rates. It would be incorrect to say that the Federal Reserve
has "control" over either of these variables. This would be
impossible in a dynamic economy such as that of the United States. Given
the number of money-like arrangements, the definition of
"money," much less its measurement, is difficult. The
monetary tools of the Federal Reserve work most directly on short-term
interest rates. Interest rates for longer maturities are indirectly
affected through the market's perception of government policy and
its economic effects. More recently, expectations of possible inflation
have been a major concern to lenders and policy makers. Economic forces
shape the level of interest rates, while governmental policies have some
effect on economic forces. Foreign interest rates have become increasingly
important. Major firms now routinely borrow in foreign markets, and
lenders are increasingly willing to hold foreign
**
debt.
**
This forces some alignment of interest rates worldwide, and reduces the
amount of control any nation has over its domestic conditions.

There are many forms of borrowing, and thus many interest rates. Borrowing
and lending arrangements include personal
**
loans,
**
credit cards,
**
mortgages,
**
various federal and municipal government obligations, corporate bonds,
and multiple other forms. Investors borrow when they trade on margin,
firms borrow by using
**
trade credit.
**
The interest rate on different borrowing arrangements will be different,
which is why the plural is used here. While economic and other variables
set the general level of interest rates, specific interest rates are
affected by other variables. While there are a multitude of factors
affecting interest rates, they are generally grouped under differences in
maturity, quality, and tax status.

RATES

Interest rates are also related to the maturity, or length of commitment,
of the arrangement. The relationship is often described by a
**
yield curve
**
showing the interest rates for various maturities. There are several
theories to explain this
**
"term structure of interest rates."
**
The first is called the "expectations theory." This theory
holds that interest rates over longer periods are dependent on the series
of short-term interest rates expected over that period—i.e.,
lenders are indifferent to the length of commitment, but require the same
expected ending
**
wealth
**
regardless of whether they lend money once for ten years or they make a
series of ten-year loans, each for one year. The motivation here is that
if this relationship did not hold, investors would prefer the alternative
with the higher ending wealth, forcing a readjustment of interest rates.
Alternately, if the relationship did not hold, investors could
**
arbitrage,
**
selling the lower yielding alternative and investing the proceeds in the
higher yielding alternative. This arbitrage would allow the arbitrager to
make a return from a net zero investment. Under this theory, the yield
curve would be upward sweeping if short-term interest rates were expected
to increase in the future, and downward sweeping if short-term interest
rates were expected to decrease in the future.

A second approach, called the "liquidity theory," suggests that investors are not indifferent as to the length of commitment. This argument suggests that lending for longer periods is more risky than short-term lending. The longer period makes prediction less accurate, and permits more opportunities for negative results. Investors prefer more liquid, shorter-term lending, and will not commit the funds for longer periods unless given a "liquidity premium" to compensate for this higher risk. Under only this approach, the yield curve would be upward sweeping at all times. Empirical observation of decreasing yield curves does not refute this theory, however, if it is combined with other theories. If the liquidity premium is superimposed on the expectation that short-term interest rates will decrease in the future, the result can be a yield curve that is still downward sweeping but less steep.

A third approach is called the "segmented markets" theory.
As we have noted, interest rates depend on supply and demand. Segmented
markets builds on this obvious statement, adding the idea that lenders and
borrowers will have a "preferred habitat," or length of
commitment. This preferred habitat comes about because of the desire of
lenders and borrowers to reduce risk by matching the maturity of assets
and
**
liabilities.
**
A lender with a liability that will come due in ten years, for example,
avoids risk by lending with a maturity of ten years; a borrower whose use
of the funds will pay off in ten years will borrow with a maturity of ten
years. Borrowers and lenders are thus reluctant to leave their preferred
maturity, and will not arbitrage. As a result, the interest rate for any
given maturity will depend on the supply and demand for that given
maturity.

In actuality, all of these theories are to some extent correct. Empirically, since World War 1I the yield curve has been predominantly upward sweeping, with long-term rates higher than short-term rates. Inverted, or downward sweeping yield curves in which long-term rates are lower than short-term rates, have been observed over shorter intervals. Long-term rates tend to have less volatility, and to move over a smaller range, than short-term rates.

RATES

The "quality" structure of interest rates describes the
effect of uncertainty about receiving the specified reward. In the face of
uncertainty about payments, lenders will demand a higher rate of return or
"risk premium." The interest rate to a particular borrower
will be the sum of a "risk-free" rate plus the risk premium.
**
Default
**
risk is not simply the failure to pay principal, but is rather a matter
of degree. There are many possibilities short of complete loss, sometimes
as small as a "skipped" or late payment. Loan arrangements
with little probability of a problem are said to be of high quality.

The higher the severity and probability of a problem, or the lower the
quality, the higher will be the risk premium. Treasury obligations, which
are direct obligations of the U.S. government and assumed to have no
default risk, are of the highest quality. Bonds issued by agencies of the
government, which are not direct government obligations, are of only
slightly lower quality since it is assumed the government would assume the
responsibility. State and local bonds, called "municipals,"
vary widely in quality depending on the characteristics of the security
and the issuer. The same variation is true of corporate bonds. These
**
securities
**
are sometimes "rated" as to quality by independent firms
such as Standard & Poor's, Moody's, Duff &
Phelps, and Fitch Investors Service. These ratings are widely used to
classify bonds and are important factors in the interest rate, or
"yield," provided to investors. Bonds below a certain rating
are often referred to as
**
junk bonds,
**
and carry a higher interest rate.

This quality structure is also apparent in
**
bank
**
loan interest rates. The
**
prime rate
**
is the rate charged to large customers with established relationships.
Borrowers with less admirable
**
credit
**
records (or smaller accounts that are comparatively more expensive) will
pay a higher rate. Collateral is also important. Unsecured personal loans,
such as credit card credit, will ordinarily pay a higher rate than car
loans, which will in turn pay more than home mortgages. An important
characteristic of loan arrangements is liquidity. An asset that can be
converted to cash quickly at a fair price is liquid; if price concessions
are required for rapid sale the asset is illiquid. Many loans have been
relatively illiquid, so that once the loan is made the creditor was locked
in. This lack of freedom of action increased the risk of the lender,
resulting in higher interest rates. More recently, a number of classes of
loans have been "securitized" by being bundled into
portfolios against which securities are issued. This added liquidity
reduces lender risk and lowers the interest rate on the underlying loan
classes.

The interest rate on bonds issued by state and local governments, called
"municipal bonds," is lower than the interest rate on
corporate bonds of the same quality. The reason for this difference is
that the interest on these debt obligations is generally exempt from
federal taxation. They are also often exempt from
**
taxes
**
of the state of issue. The real rate of increase in purchasing power from
taxable federal and corporate debt instruments will be reduced by the
taxes:

Since interest rates reflect the real rate or increase in purchasing power, taxable and nontaxable debt will have the same after-tax rate of return. This equilibrium will not hold for all investors because of differing tax rates. For investors with high tax rates, the after-tax rate of return on municipals may be higher, while for investors with low tax rates the return on corporate debt may be higher.

Another tax effect comes about because of the tax deductibility of some interest payments on personal taxes. The tax deductibility of interest on home mortgages effectively lowers the interest rate. This is reflected in the rapid increase in mortgage-based loans after interest on consumer debts was no longer tax deductible.

*
[
*
*
David
*
*
E
*
*
Upton
*
*
]
*

Reilly, Frank K., and Keith C. Brown.
*
Investment Analysis and Portfolio Management.
*
5th ed. Fort Worth, TX: Dryden Press, 1997.

Van Home, James C.
*
Financial Market Rates and Flows.
*
5th ed. Upper Saddle River, NJ: Prentice Hall, 1998.

Also read article about **Interest Rates** from Wikipedia

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